I think most of the strain is going to be in the brakes and the suspension... the tranny just works against the extra weight as if you had trunk full of groceries (added weight = added work). But the increased rotational weight and the added weight on the suspension components is worse.
One other thing to consider is that the larger wheels will typically be heavier, but the tire that you'd use is lower profile and usually weighs less. It's not enough to completely offset the gains you'd get from using smaller, lighter wheels, but it does make up for some of that added weight in the wheels.
That web site didn't have the weight for MY wheel but, had the weights for almost every other wheel made by Enkei. Mine is the RS5 in an 18" if anyone wants to try and find the weight of them.
About tire weight. Even though they are lower profile meaning less rubber but, most everbody chooses wider tires. Meaning more rubber to make up for the low pros. Plus who knows about the different componds the tires are made out of. It could change the weight a bit.